Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I

Percentage Accurate: 95.6% → 97.4%

Time: 3.9s

Alternatives: 5

Speedup: 0.6×

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - (y * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Python

def code(x, y, z):
	return x * (1.0 - (y * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(y * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (y * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - (y * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (y * z));
}

Python

def code(x, y, z):
	return x * (1.0 - (y * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(y * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (y * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -5e+113) (* y (* z (- x))) (- x (* x (* y z)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+113) {
		tmp = y * (z * -x);
	} else {
		tmp = x - (x * (y * z));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y * z) <= (-5d+113)) then
        tmp = y * (z * -x)
    else
        tmp = x - (x * (y * z))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+113) {
		tmp = y * (z * -x);
	} else {
		tmp = x - (x * (y * z));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -5e+113:
		tmp = y * (z * -x)
	else:
		tmp = x - (x * (y * z))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -5e+113)
		tmp = Float64(y * Float64(z * Float64(-x)));
	else
		tmp = Float64(x - Float64(x * Float64(y * z)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -5e+113)
		tmp = y * (z * -x);
	else
		tmp = x - (x * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -5e+113], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5e113

   1. Initial program 87.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Step-by-step derivation

      1. remove-double-neg 87.6%

         \[\leadsto \color{blue}{-\left(-x \cdot \left(1 - y \cdot z\right)\right)} \]

      2. distribute-lft-neg-out 87.6%

         \[\leadsto -\color{blue}{\left(-x\right) \cdot \left(1 - y \cdot z\right)} \]

      3. neg-mul-1 87.6%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right)} \]

      4. *-commutative 87.6%

         \[\leadsto \color{blue}{\left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right) \cdot -1} \]

      5. associate-*r* 87.6%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

      6. distribute-lft-neg-in 87.6%

         \[\leadsto \color{blue}{-x \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

      7. distribute-rgt-neg-out 87.6%

         \[\leadsto \color{blue}{x \cdot \left(-\left(1 - y \cdot z\right) \cdot -1\right)} \]

      8. *-commutative 87.6%

         \[\leadsto x \cdot \left(-\color{blue}{-1 \cdot \left(1 - y \cdot z\right)}\right) \]

      9. neg-mul-1 87.6%

         \[\leadsto x \cdot \left(-\color{blue}{\left(-\left(1 - y \cdot z\right)\right)}\right) \]

      10. remove-double-neg 87.6%

          \[\leadsto x \cdot \color{blue}{\left(1 - y \cdot z\right)} \]

      11. cancel-sign-sub-inv 87.6%

          \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y\right) \cdot z\right)} \]

      12. +-commutative 87.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(-y\right) \cdot z + 1\right)} \]

      13. distribute-lft-neg-out 87.6%

          \[\leadsto x \cdot \left(\color{blue}{\left(-y \cdot z\right)} + 1\right) \]

      14. metadata-eval 87.6%

          \[\leadsto x \cdot \left(\left(-y \cdot z\right) + \color{blue}{\left(--1\right)}\right) \]

      15. distribute-neg-in 87.6%

          \[\leadsto x \cdot \color{blue}{\left(-\left(y \cdot z + -1\right)\right)} \]

      16. fma-def 87.6%

          \[\leadsto x \cdot \left(-\color{blue}{\mathsf{fma}\left(y, z, -1\right)}\right) \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{x \cdot \left(-\mathsf{fma}\left(y, z, -1\right)\right)} \]

   4. Taylor expanded in y around inf 97.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 97.5%

         \[\leadsto \color{blue}{-y \cdot \left(z \cdot x\right)} \]

      2. distribute-rgt-neg-in 97.5%

         \[\leadsto \color{blue}{y \cdot \left(-z \cdot x\right)} \]

      3. distribute-rgt-neg-in 97.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot \left(-x\right)\right)} \]

   6. Simplified 97.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-x\right)\right)} \]

   if -5e113 < (*.f64 y z)

   1. Initial program 98.2%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Step-by-step derivation

      1. remove-double-neg 98.2%

         \[\leadsto \color{blue}{-\left(-x \cdot \left(1 - y \cdot z\right)\right)} \]

      2. distribute-lft-neg-out 98.2%

         \[\leadsto -\color{blue}{\left(-x\right) \cdot \left(1 - y \cdot z\right)} \]

      3. neg-mul-1 98.2%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right)} \]

      4. *-commutative 98.2%

         \[\leadsto \color{blue}{\left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right) \cdot -1} \]

      5. associate-*r* 98.2%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

      6. distribute-lft-neg-in 98.2%

         \[\leadsto \color{blue}{-x \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

      7. distribute-rgt-neg-out 98.2%

         \[\leadsto \color{blue}{x \cdot \left(-\left(1 - y \cdot z\right) \cdot -1\right)} \]

      8. *-commutative 98.2%

         \[\leadsto x \cdot \left(-\color{blue}{-1 \cdot \left(1 - y \cdot z\right)}\right) \]

      9. neg-mul-1 98.2%

         \[\leadsto x \cdot \left(-\color{blue}{\left(-\left(1 - y \cdot z\right)\right)}\right) \]

      10. remove-double-neg 98.2%

          \[\leadsto x \cdot \color{blue}{\left(1 - y \cdot z\right)} \]

      11. cancel-sign-sub-inv 98.2%

          \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y\right) \cdot z\right)} \]

      12. +-commutative 98.2%

          \[\leadsto x \cdot \color{blue}{\left(\left(-y\right) \cdot z + 1\right)} \]

      13. distribute-lft-neg-out 98.2%

          \[\leadsto x \cdot \left(\color{blue}{\left(-y \cdot z\right)} + 1\right) \]

      14. metadata-eval 98.2%

          \[\leadsto x \cdot \left(\left(-y \cdot z\right) + \color{blue}{\left(--1\right)}\right) \]

      15. distribute-neg-in 98.2%

          \[\leadsto x \cdot \color{blue}{\left(-\left(y \cdot z + -1\right)\right)} \]

      16. fma-def 98.2%

          \[\leadsto x \cdot \left(-\color{blue}{\mathsf{fma}\left(y, z, -1\right)}\right) \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{x \cdot \left(-\mathsf{fma}\left(y, z, -1\right)\right)} \]
   4. Step-by-step derivation

      1. fma-udef 98.2%

         \[\leadsto x \cdot \left(-\color{blue}{\left(y \cdot z + -1\right)}\right) \]

      2. distribute-neg-in 98.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(-y \cdot z\right) + \left(--1\right)\right)} \]

      3. metadata-eval 98.2%

         \[\leadsto x \cdot \left(\left(-y \cdot z\right) + \color{blue}{1}\right) \]

      4. +-commutative 98.2%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y \cdot z\right)\right)} \]

      5. distribute-rgt-in 98.2%

         \[\leadsto \color{blue}{1 \cdot x + \left(-y \cdot z\right) \cdot x} \]

      6. *-un-lft-identity 98.2%

         \[\leadsto \color{blue}{x} + \left(-y \cdot z\right) \cdot x \]

      7. *-commutative 98.2%

         \[\leadsto x + \left(-\color{blue}{z \cdot y}\right) \cdot x \]

      8. distribute-rgt-neg-in 98.2%

         \[\leadsto x + \color{blue}{\left(z \cdot \left(-y\right)\right)} \cdot x \]

   5. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{x + \left(z \cdot \left(-y\right)\right) \cdot x} \]
   6. Step-by-step derivation

      1. distribute-rgt-neg-out 98.2%

         \[\leadsto x + \color{blue}{\left(-z \cdot y\right)} \cdot x \]

      2. *-commutative 98.2%

         \[\leadsto x + \left(-\color{blue}{y \cdot z}\right) \cdot x \]

      3. cancel-sign-sub-inv 98.2%

         \[\leadsto \color{blue}{x - \left(y \cdot z\right) \cdot x} \]

      4. *-commutative 98.2%

         \[\leadsto x - \color{blue}{x \cdot \left(y \cdot z\right)} \]

      5. *-commutative 98.2%

         \[\leadsto x - x \cdot \color{blue}{\left(z \cdot y\right)} \]

   7. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{x - x \cdot \left(z \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 2: 97.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -5e+113) (* y (* z (- x))) (* x (- 1.0 (* y z)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+113) {
		tmp = y * (z * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y * z) <= (-5d+113)) then
        tmp = y * (z * -x)
    else
        tmp = x * (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+113) {
		tmp = y * (z * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -5e+113:
		tmp = y * (z * -x)
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -5e+113)
		tmp = Float64(y * Float64(z * Float64(-x)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -5e+113)
		tmp = y * (z * -x);
	else
		tmp = x * (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -5e+113], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5e113

   1. Initial program 87.6%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Step-by-step derivation

      1. remove-double-neg 87.6%

         \[\leadsto \color{blue}{-\left(-x \cdot \left(1 - y \cdot z\right)\right)} \]

      2. distribute-lft-neg-out 87.6%

         \[\leadsto -\color{blue}{\left(-x\right) \cdot \left(1 - y \cdot z\right)} \]

      3. neg-mul-1 87.6%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right)} \]

      4. *-commutative 87.6%

         \[\leadsto \color{blue}{\left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right) \cdot -1} \]

      5. associate-*r* 87.6%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

      6. distribute-lft-neg-in 87.6%

         \[\leadsto \color{blue}{-x \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

      7. distribute-rgt-neg-out 87.6%

         \[\leadsto \color{blue}{x \cdot \left(-\left(1 - y \cdot z\right) \cdot -1\right)} \]

      8. *-commutative 87.6%

         \[\leadsto x \cdot \left(-\color{blue}{-1 \cdot \left(1 - y \cdot z\right)}\right) \]

      9. neg-mul-1 87.6%

         \[\leadsto x \cdot \left(-\color{blue}{\left(-\left(1 - y \cdot z\right)\right)}\right) \]

      10. remove-double-neg 87.6%

          \[\leadsto x \cdot \color{blue}{\left(1 - y \cdot z\right)} \]

      11. cancel-sign-sub-inv 87.6%

          \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y\right) \cdot z\right)} \]

      12. +-commutative 87.6%

          \[\leadsto x \cdot \color{blue}{\left(\left(-y\right) \cdot z + 1\right)} \]

      13. distribute-lft-neg-out 87.6%

          \[\leadsto x \cdot \left(\color{blue}{\left(-y \cdot z\right)} + 1\right) \]

      14. metadata-eval 87.6%

          \[\leadsto x \cdot \left(\left(-y \cdot z\right) + \color{blue}{\left(--1\right)}\right) \]

      15. distribute-neg-in 87.6%

          \[\leadsto x \cdot \color{blue}{\left(-\left(y \cdot z + -1\right)\right)} \]

      16. fma-def 87.6%

          \[\leadsto x \cdot \left(-\color{blue}{\mathsf{fma}\left(y, z, -1\right)}\right) \]

   3. Simplified 87.6%

      \[\leadsto \color{blue}{x \cdot \left(-\mathsf{fma}\left(y, z, -1\right)\right)} \]

   4. Taylor expanded in y around inf 97.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 97.5%

         \[\leadsto \color{blue}{-y \cdot \left(z \cdot x\right)} \]

      2. distribute-rgt-neg-in 97.5%

         \[\leadsto \color{blue}{y \cdot \left(-z \cdot x\right)} \]

      3. distribute-rgt-neg-in 97.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot \left(-x\right)\right)} \]

   6. Simplified 97.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-x\right)\right)} \]

   if -5e113 < (*.f64 y z)

   1. Initial program 98.2%

      \[x \cdot \left(1 - y \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+113}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 3: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-148} \lor \neg \left(z \leq 3.1 \cdot 10^{+64}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.9e-148) (not (<= z 3.1e+64))) (* x (* y (- z))) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e-148) || !(z <= 3.1e+64)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.9d-148)) .or. (.not. (z <= 3.1d+64))) then
        tmp = x * (y * -z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e-148) || !(z <= 3.1e+64)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.9e-148) or not (z <= 3.1e+64):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.9e-148) || !(z <= 3.1e+64))
		tmp = Float64(x * Float64(y * Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.9e-148) || ~((z <= 3.1e+64)))
		tmp = x * (y * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -1.9e-148], N[Not[LessEqual[z, 3.1e+64]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.90000000000000007e-148 or 3.0999999999999999e64 < z

   1. Initial program 94.3%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 59.8%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(y \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 59.8%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot z\right)} \]

      2. neg-mul-1 59.8%

         \[\leadsto x \cdot \left(\color{blue}{\left(-y\right)} \cdot z\right) \]

      3. *-commutative 59.8%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(-y\right)\right)} \]

   4. Simplified 59.8%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(-y\right)\right)} \]

   if -1.90000000000000007e-148 < z < 3.0999999999999999e64

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Step-by-step derivation

      1. remove-double-neg 99.9%

         \[\leadsto \color{blue}{-\left(-x \cdot \left(1 - y \cdot z\right)\right)} \]

      2. distribute-lft-neg-out 99.9%

         \[\leadsto -\color{blue}{\left(-x\right) \cdot \left(1 - y \cdot z\right)} \]

      3. neg-mul-1 99.9%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right)} \]

      4. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right) \cdot -1} \]

      5. associate-*r* 99.9%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

      6. distribute-lft-neg-in 99.9%

         \[\leadsto \color{blue}{-x \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

      7. distribute-rgt-neg-out 99.9%

         \[\leadsto \color{blue}{x \cdot \left(-\left(1 - y \cdot z\right) \cdot -1\right)} \]

      8. *-commutative 99.9%

         \[\leadsto x \cdot \left(-\color{blue}{-1 \cdot \left(1 - y \cdot z\right)}\right) \]

      9. neg-mul-1 99.9%

         \[\leadsto x \cdot \left(-\color{blue}{\left(-\left(1 - y \cdot z\right)\right)}\right) \]

      10. remove-double-neg 99.9%

          \[\leadsto x \cdot \color{blue}{\left(1 - y \cdot z\right)} \]

      11. cancel-sign-sub-inv 99.9%

          \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y\right) \cdot z\right)} \]

      12. +-commutative 99.9%

          \[\leadsto x \cdot \color{blue}{\left(\left(-y\right) \cdot z + 1\right)} \]

      13. distribute-lft-neg-out 99.9%

          \[\leadsto x \cdot \left(\color{blue}{\left(-y \cdot z\right)} + 1\right) \]

      14. metadata-eval 99.9%

          \[\leadsto x \cdot \left(\left(-y \cdot z\right) + \color{blue}{\left(--1\right)}\right) \]

      15. distribute-neg-in 99.9%

          \[\leadsto x \cdot \color{blue}{\left(-\left(y \cdot z + -1\right)\right)} \]

      16. fma-def 99.9%

          \[\leadsto x \cdot \left(-\color{blue}{\mathsf{fma}\left(y, z, -1\right)}\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(-\mathsf{fma}\left(y, z, -1\right)\right)} \]

   4. Taylor expanded in y around 0 77.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-148} \lor \neg \left(z \leq 3.1 \cdot 10^{+64}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-148}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -1.9e-148)
   (* x (* y (- z)))
   (if (<= z 2.05e+64) x (* y (* z (- x))))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e-148) {
		tmp = x * (y * -z);
	} else if (z <= 2.05e+64) {
		tmp = x;
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.9d-148)) then
        tmp = x * (y * -z)
    else if (z <= 2.05d+64) then
        tmp = x
    else
        tmp = y * (z * -x)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e-148) {
		tmp = x * (y * -z);
	} else if (z <= 2.05e+64) {
		tmp = x;
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if z <= -1.9e-148:
		tmp = x * (y * -z)
	elif z <= 2.05e+64:
		tmp = x
	else:
		tmp = y * (z * -x)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (z <= -1.9e-148)
		tmp = Float64(x * Float64(y * Float64(-z)));
	elseif (z <= 2.05e+64)
		tmp = x;
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.9e-148)
		tmp = x * (y * -z);
	elseif (z <= 2.05e+64)
		tmp = x;
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[z, -1.9e-148], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+64], x, N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000007e-148

   1. Initial program 96.1%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 53.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \left(y \cdot z\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 53.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot y\right) \cdot z\right)} \]

      2. neg-mul-1 53.7%

         \[\leadsto x \cdot \left(\color{blue}{\left(-y\right)} \cdot z\right) \]

      3. *-commutative 53.7%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(-y\right)\right)} \]

   4. Simplified 53.7%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(-y\right)\right)} \]

   if -1.90000000000000007e-148 < z < 2.04999999999999989e64

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Step-by-step derivation

      1. remove-double-neg 99.9%

         \[\leadsto \color{blue}{-\left(-x \cdot \left(1 - y \cdot z\right)\right)} \]

      2. distribute-lft-neg-out 99.9%

         \[\leadsto -\color{blue}{\left(-x\right) \cdot \left(1 - y \cdot z\right)} \]

      3. neg-mul-1 99.9%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right)} \]

      4. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right) \cdot -1} \]

      5. associate-*r* 99.9%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

      6. distribute-lft-neg-in 99.9%

         \[\leadsto \color{blue}{-x \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

      7. distribute-rgt-neg-out 99.9%

         \[\leadsto \color{blue}{x \cdot \left(-\left(1 - y \cdot z\right) \cdot -1\right)} \]

      8. *-commutative 99.9%

         \[\leadsto x \cdot \left(-\color{blue}{-1 \cdot \left(1 - y \cdot z\right)}\right) \]

      9. neg-mul-1 99.9%

         \[\leadsto x \cdot \left(-\color{blue}{\left(-\left(1 - y \cdot z\right)\right)}\right) \]

      10. remove-double-neg 99.9%

          \[\leadsto x \cdot \color{blue}{\left(1 - y \cdot z\right)} \]

      11. cancel-sign-sub-inv 99.9%

          \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y\right) \cdot z\right)} \]

      12. +-commutative 99.9%

          \[\leadsto x \cdot \color{blue}{\left(\left(-y\right) \cdot z + 1\right)} \]

      13. distribute-lft-neg-out 99.9%

          \[\leadsto x \cdot \left(\color{blue}{\left(-y \cdot z\right)} + 1\right) \]

      14. metadata-eval 99.9%

          \[\leadsto x \cdot \left(\left(-y \cdot z\right) + \color{blue}{\left(--1\right)}\right) \]

      15. distribute-neg-in 99.9%

          \[\leadsto x \cdot \color{blue}{\left(-\left(y \cdot z + -1\right)\right)} \]

      16. fma-def 99.9%

          \[\leadsto x \cdot \left(-\color{blue}{\mathsf{fma}\left(y, z, -1\right)}\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(-\mathsf{fma}\left(y, z, -1\right)\right)} \]

   4. Taylor expanded in y around 0 77.2%

      \[\leadsto \color{blue}{x} \]

   if 2.04999999999999989e64 < z

   1. Initial program 90.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Step-by-step derivation

      1. remove-double-neg 90.9%

         \[\leadsto \color{blue}{-\left(-x \cdot \left(1 - y \cdot z\right)\right)} \]

      2. distribute-lft-neg-out 90.9%

         \[\leadsto -\color{blue}{\left(-x\right) \cdot \left(1 - y \cdot z\right)} \]

      3. neg-mul-1 90.9%

         \[\leadsto \color{blue}{-1 \cdot \left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right)} \]

      4. *-commutative 90.9%

         \[\leadsto \color{blue}{\left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right) \cdot -1} \]

      5. associate-*r* 90.9%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

      6. distribute-lft-neg-in 90.9%

         \[\leadsto \color{blue}{-x \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

      7. distribute-rgt-neg-out 90.9%

         \[\leadsto \color{blue}{x \cdot \left(-\left(1 - y \cdot z\right) \cdot -1\right)} \]

      8. *-commutative 90.9%

         \[\leadsto x \cdot \left(-\color{blue}{-1 \cdot \left(1 - y \cdot z\right)}\right) \]

      9. neg-mul-1 90.9%

         \[\leadsto x \cdot \left(-\color{blue}{\left(-\left(1 - y \cdot z\right)\right)}\right) \]

      10. remove-double-neg 90.9%

          \[\leadsto x \cdot \color{blue}{\left(1 - y \cdot z\right)} \]

      11. cancel-sign-sub-inv 90.9%

          \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y\right) \cdot z\right)} \]

      12. +-commutative 90.9%

          \[\leadsto x \cdot \color{blue}{\left(\left(-y\right) \cdot z + 1\right)} \]

      13. distribute-lft-neg-out 90.9%

          \[\leadsto x \cdot \left(\color{blue}{\left(-y \cdot z\right)} + 1\right) \]

      14. metadata-eval 90.9%

          \[\leadsto x \cdot \left(\left(-y \cdot z\right) + \color{blue}{\left(--1\right)}\right) \]

      15. distribute-neg-in 90.9%

          \[\leadsto x \cdot \color{blue}{\left(-\left(y \cdot z + -1\right)\right)} \]

      16. fma-def 90.9%

          \[\leadsto x \cdot \left(-\color{blue}{\mathsf{fma}\left(y, z, -1\right)}\right) \]

   3. Simplified 90.9%

      \[\leadsto \color{blue}{x \cdot \left(-\mathsf{fma}\left(y, z, -1\right)\right)} \]

   4. Taylor expanded in y around inf 77.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot x\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 77.9%

         \[\leadsto \color{blue}{-y \cdot \left(z \cdot x\right)} \]

      2. distribute-rgt-neg-in 77.9%

         \[\leadsto \color{blue}{y \cdot \left(-z \cdot x\right)} \]

      3. distribute-rgt-neg-in 77.9%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot \left(-x\right)\right)} \]

   6. Simplified 77.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-148}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 5: 50.8% accurate, 7.0× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ x \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 x)

C

assert(y < z);
double code(double x, double y, double z) {
	return x;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	return x;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	return x

Julia

y, z = sort([y, z])
function code(x, y, z)
	return x
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := x

Derivation

1. Initial program 96.6%

   \[x \cdot \left(1 - y \cdot z\right) \]
2. Step-by-step derivation

   1. remove-double-neg 96.6%

      \[\leadsto \color{blue}{-\left(-x \cdot \left(1 - y \cdot z\right)\right)} \]

   2. distribute-lft-neg-out 96.6%

      \[\leadsto -\color{blue}{\left(-x\right) \cdot \left(1 - y \cdot z\right)} \]

   3. neg-mul-1 96.6%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right)} \]

   4. *-commutative 96.6%

      \[\leadsto \color{blue}{\left(\left(-x\right) \cdot \left(1 - y \cdot z\right)\right) \cdot -1} \]

   5. associate-*r* 96.6%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

   6. distribute-lft-neg-in 96.6%

      \[\leadsto \color{blue}{-x \cdot \left(\left(1 - y \cdot z\right) \cdot -1\right)} \]

   7. distribute-rgt-neg-out 96.6%

      \[\leadsto \color{blue}{x \cdot \left(-\left(1 - y \cdot z\right) \cdot -1\right)} \]

   8. *-commutative 96.6%

      \[\leadsto x \cdot \left(-\color{blue}{-1 \cdot \left(1 - y \cdot z\right)}\right) \]

   9. neg-mul-1 96.6%

      \[\leadsto x \cdot \left(-\color{blue}{\left(-\left(1 - y \cdot z\right)\right)}\right) \]

   10. remove-double-neg 96.6%

       \[\leadsto x \cdot \color{blue}{\left(1 - y \cdot z\right)} \]

   11. cancel-sign-sub-inv 96.6%

       \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y\right) \cdot z\right)} \]

   12. +-commutative 96.6%

       \[\leadsto x \cdot \color{blue}{\left(\left(-y\right) \cdot z + 1\right)} \]

   13. distribute-lft-neg-out 96.6%

       \[\leadsto x \cdot \left(\color{blue}{\left(-y \cdot z\right)} + 1\right) \]

   14. metadata-eval 96.6%

       \[\leadsto x \cdot \left(\left(-y \cdot z\right) + \color{blue}{\left(--1\right)}\right) \]

   15. distribute-neg-in 96.6%

       \[\leadsto x \cdot \color{blue}{\left(-\left(y \cdot z + -1\right)\right)} \]

   16. fma-def 96.6%

       \[\leadsto x \cdot \left(-\color{blue}{\mathsf{fma}\left(y, z, -1\right)}\right) \]

3. Simplified 96.6%

   \[\leadsto \color{blue}{x \cdot \left(-\mathsf{fma}\left(y, z, -1\right)\right)} \]

4. Taylor expanded in y around 0 52.3%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 52.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))